Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Multirate Digital Signal Processing
Multirate Digital Signal Processing
Signal Processing with Lapped Transforms
Signal Processing with Lapped Transforms
Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets
Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets
A modulated complex lapped transform and its applications to audio processing
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Lapped directional transform: a new transform for spectral image analysis
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 06
One- and two-level filter-bank convolvers
IEEE Transactions on Signal Processing
Bifrequency and bispectrum maps: a new look at multirate systemswith stochastic inputs
IEEE Transactions on Signal Processing
A translation-invariant wavelet representation algorithm withapplications
IEEE Transactions on Signal Processing
Optimization of filter banks using cyclostationary spectralanalysis
IEEE Transactions on Signal Processing
Wavelet footprints: theory, algorithms, and applications
IEEE Transactions on Signal Processing
Motion estimation using low-band-shift method for wavelet-based moving-picture coding
IEEE Transactions on Image Processing
Polyphase antialiasing in resampling of images
IEEE Transactions on Image Processing
An Orientation-Selective Orthogonal Lapped Transform
IEEE Transactions on Image Processing
Rate Bounds on SSIM Index of Quantized Images
IEEE Transactions on Image Processing
Wavelet filter evaluation for image compression
IEEE Transactions on Image Processing
Comparison of wavelets for multiresolution motion estimation
IEEE Transactions on Circuits and Systems for Video Technology
Texture classification by modeling joint distributions of local patterns with Gaussian mixtures
IEEE Transactions on Image Processing
Hi-index | 35.69 |
Critically sampled multirate FIR filter banks exhibit periodically shift variant behavior caused by nonideal antialiasing filtering in the decimation stage. We assess their shift variance quantitatively by analysing changes in the output signal when the filter bank operator and shift operator are interchanged. We express these changes by a so-called commutator. We then derive a sharp upper bound for shift variance via the operator norm of the commutator, which is independent of the input signal. Its core is an eigensystem analysis carried out within a frequency domain formulation of the commutator, leading to a matrix norm which depends on frequency. This bound can be regarded as a worst case instance holding for all input signals. For two channel FIR filter banks with perfect reconstruction (PR), we show that the bound is predominantly determined by the structure of the filter bank rather than by the type of filters used. Moreover, the framework allows to identify the signals for which the upper bound is almost reached as so-called near maximizers of the frequency-dependent matrix norm. For unitary PR filter banks, these near maximizers are shown to be narrow-band signals. To complement this worst-case bound, we derive an additional bound on shift variance for input signals with given amplitude spectra, where we use wide-band model spectra instead of narrow-band signals. Like the operator norm, this additional bound is based on the above frequency-dependent matrix norm.We provide results for various critically sampled two-channel filter banks, such as quadrature mirror filters, PR conjugated quadrature filters, wavelets, and biorthogonal filters banks.